{"product_id":"compositional-data-analysis-9780470711354","title":"Compositional Data Analysis","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eIt is difficult to imagine that the statistical analysis of compositional data has been a major issue of concern for more than 100 years. It is even more difficult to realize that so many statisticians and users of statistics are unaware of the particular problems affecting compositional data, as well as their solutions.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cb\u003ePreface xvii\u003c\/b\u003e  \u003cp\u003e\u003cb\u003eList of Contributors xix\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart I Introduction\u003c\/b\u003e 1\u003c\/p\u003e \u003cp\u003e1 A Short History of Compositional Data Analysis 3\u003cbr\u003e \u003ci\u003eJohn Bacon-Shone\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e1.1 Introduction 3\u003c\/p\u003e \u003cp\u003e1.2 Spurious Correlation 3\u003c\/p\u003e \u003cp\u003e1.3 Log and Log-Ratio Transforms 4\u003c\/p\u003e \u003cp\u003e1.4 Subcompositional Dependence 5\u003c\/p\u003e \u003cp\u003e1.5 alr, clr, ilr: Which Transformation to Choose? 5\u003c\/p\u003e \u003cp\u003e1.6 Principles, Perturbations and Back to the Simplex 6\u003c\/p\u003e \u003cp\u003e1.7 Biplots and Singular Value Decompositions 7\u003c\/p\u003e \u003cp\u003e1.8 Mixtures 7\u003c\/p\u003e \u003cp\u003e1.9 Discrete Compositions 8\u003c\/p\u003e \u003cp\u003e1.10 Compositional Processes 8\u003c\/p\u003e \u003cp\u003e1.11 Structural, Counting and Rounded Zeros 8\u003c\/p\u003e \u003cp\u003e1.12 Conclusion 9\u003c\/p\u003e \u003cp\u003eAcknowledgement 9\u003c\/p\u003e \u003cp\u003eReferences 9\u003c\/p\u003e \u003cp\u003e2 Basic Concepts and Procedures 12\u003cbr\u003e \u003ci\u003eJuan Jos´e Egozcue and Vera Pawlowsky-Glahn\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 12\u003c\/p\u003e \u003cp\u003e2.2 Election Data and Raw Analysis 13\u003c\/p\u003e \u003cp\u003e2.3 The Compositional Alternative 15\u003c\/p\u003e \u003cp\u003e2.3.1 Scale Invariance: Vectors with Proportional Positive Components Represent the Same Composition 15\u003c\/p\u003e \u003cp\u003e2.3.2 Subcompositional Coherence: Analyses Concerning a Subset of Parts Must Not Depend on Other Non-Involved Parts 16\u003c\/p\u003e \u003cp\u003e2.3.3 Permutation Invariance: The Conclusions of a Compositional Analysis Should Not Depend on the Order of the Parts 17\u003c\/p\u003e \u003cp\u003e2.4 Geometric Settings 17\u003c\/p\u003e \u003cp\u003e2.5 Centre and Variability 22\u003c\/p\u003e \u003cp\u003e2.6 Conclusion 27\u003c\/p\u003e \u003cp\u003eAcknowledgements 27\u003c\/p\u003e \u003cp\u003eReferences 27\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II Theory – Statistical Modelling\u003c\/b\u003e 29\u003c\/p\u003e \u003cp\u003e3 The Principle of Working on Coordinates 31\u003cbr\u003e \u003ci\u003eGlòria Mateu-Figueras, Vera Pawlowsky-Glahn and Juan José Egozcue\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 31\u003c\/p\u003e \u003cp\u003e3.2 The Role of Coordinates in Statistics 32\u003c\/p\u003e \u003cp\u003e3.3 The Simplex 33\u003c\/p\u003e \u003cp\u003e3.3.1 Basis of the Simplex 34\u003c\/p\u003e \u003cp\u003e3.3.2 Working on Orthonormal Coordinates 35\u003c\/p\u003e \u003cp\u003e3.4 \u003ci\u003eMove\u003c\/i\u003e or \u003ci\u003eStay\u003c\/i\u003e in the Simplex 38\u003c\/p\u003e \u003cp\u003e3.5 Conclusions 40\u003c\/p\u003e \u003cp\u003eAcknowledgements 41\u003c\/p\u003e \u003cp\u003eReferences 41\u003c\/p\u003e \u003cp\u003e4 Dealing with Zeros 43\u003cbr\u003e \u003ci\u003eJosep Antoni Martún-Fernández, Javier Palarea-Albaladejo and Ricardo Antonio Olea\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 43\u003c\/p\u003e \u003cp\u003e4.2 Rounded Zeros 44\u003c\/p\u003e \u003cp\u003e4.2.1 Non-Parametric Replacement of Rounded Zeros 45\u003c\/p\u003e \u003cp\u003e4.2.2 Parametric Modified EM Algorithm for Rounded Zeros 47\u003c\/p\u003e \u003cp\u003e4.3 Count Zeros 50\u003c\/p\u003e \u003cp\u003e4.4 Essential Zeros 53\u003c\/p\u003e \u003cp\u003e4.5 Difficulties, Troubles and Challenges 55\u003c\/p\u003e \u003cp\u003eAcknowledgements 57\u003c\/p\u003e \u003cp\u003eReferences 57\u003c\/p\u003e \u003cp\u003e5 Robust Statistical Analysis 59\u003cbr\u003e \u003ci\u003ePeter Filzmoser and Karel Hron\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 59\u003c\/p\u003e \u003cp\u003e5.2 Elements of Robust Statistics from a Compositional Point of View 60\u003c\/p\u003e \u003cp\u003e5.3 Robust Methods for Compositional Data 63\u003c\/p\u003e \u003cp\u003e5.3.1 Multivariate Outlier Detection 64\u003c\/p\u003e \u003cp\u003e5.3.2 Principal Component Analysis 64\u003c\/p\u003e \u003cp\u003e5.3.3 Discriminant Analysis 65\u003c\/p\u003e \u003cp\u003e5.4 Case Studies 66\u003c\/p\u003e \u003cp\u003e5.4.1 Multivariate Outlier Detection 66\u003c\/p\u003e \u003cp\u003e5.4.2 Principal Component Analysis 68\u003c\/p\u003e \u003cp\u003e5.4.3 Discriminant Analysis 68\u003c\/p\u003e \u003cp\u003e5.5 Summary 70\u003c\/p\u003e \u003cp\u003eAcknowledgement 71\u003c\/p\u003e \u003cp\u003eReferences 71\u003c\/p\u003e \u003cp\u003e6 Geostatistics for Compositions 73\u003cbr\u003e \u003ci\u003eRaimon Tolosana-Delgado, Karl Gerald van den Boogaart and Vera Pawlowsky-Glahn\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 73\u003c\/p\u003e \u003cp\u003e6.2 A Brief Summary of Geostatistics 74\u003c\/p\u003e \u003cp\u003e6.3 Cokriging of Regionalised Compositions 76\u003c\/p\u003e \u003cp\u003e6.4 Structural Analysis of Regionalised Composition 76\u003c\/p\u003e \u003cp\u003e6.5 Dealing with Zeros: Replacement Strategies and Simplicial Indicator Cokriging 78\u003c\/p\u003e \u003cp\u003e6.6 Application 79\u003c\/p\u003e \u003cp\u003e6.6.1 Delimiting the Body: Simplicial Indicator Kriging 81\u003c\/p\u003e \u003cp\u003e6.6.2 Interpolating the Oil–Brine–Solid Content 82\u003c\/p\u003e \u003cp\u003e6.7 Conclusions 84\u003c\/p\u003e \u003cp\u003eAcknowledgements 84\u003c\/p\u003e \u003cp\u003eReferences 84\u003c\/p\u003e \u003cp\u003e7 Compositional VARIMA Time Series 87\u003cbr\u003e \u003ci\u003eCarles Barceló-Vidal, Lucúa Aguilar and Josep Antoni Martún-Fernández\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 87\u003c\/p\u003e \u003cp\u003e7.2 The Simplex \u003ci\u003eSD\u003c\/i\u003e as a Compositional Space 89\u003c\/p\u003e \u003cp\u003e7.2.1 Basic Concepts and Notation 89\u003c\/p\u003e \u003cp\u003e7.2.2 The Covariance Structure on the Simplex 90\u003c\/p\u003e \u003cp\u003e7.3 Compositional Time Series Models 91\u003c\/p\u003e \u003cp\u003e7.3.1 \u003ci\u003eC\u003c\/i\u003e-Stationary Processes 92\u003c\/p\u003e \u003cp\u003e7.3.2 \u003ci\u003eC\u003c\/i\u003e-VARIMA Processes 93\u003c\/p\u003e \u003cp\u003e7.4 CTS Modelling: An Example 94\u003c\/p\u003e \u003cp\u003e7.4.1 Expenditure Shares in the UK 94\u003c\/p\u003e \u003cp\u003e7.4.2 Model Selection 95\u003c\/p\u003e \u003cp\u003e7.4.3 Estimation of Parameters 96\u003c\/p\u003e \u003cp\u003e7.4.4 Interpretation and Comparison 96\u003c\/p\u003e \u003cp\u003e7.5 Discussion 99\u003c\/p\u003e \u003cp\u003eAcknowledgements 99\u003c\/p\u003e \u003cp\u003eReferences 100\u003c\/p\u003e \u003cp\u003eAppendix 102\u003c\/p\u003e \u003cp\u003e8 Compositional Data and Correspondence Analysis 104\u003cbr\u003e \u003ci\u003eMichael Greenacre\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 104\u003c\/p\u003e \u003cp\u003e8.2 Comparative Technical Definitions 105\u003c\/p\u003e \u003cp\u003e8.3 Properties and Interpretation of LRA and CA 107\u003c\/p\u003e \u003cp\u003e8.4 Application to Fatty Acid Compositional Data 107\u003c\/p\u003e \u003cp\u003e8.5 Discussion and Conclusions 111\u003c\/p\u003e \u003cp\u003eAcknowledgements 112\u003c\/p\u003e \u003cp\u003eReferences 112\u003c\/p\u003e \u003cp\u003e9 Use of Survey Weights for the Analysis of Compositional Data 114\u003cbr\u003e \u003ci\u003eMonique Graf\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 114\u003c\/p\u003e \u003cp\u003e9.2 Elements of Survey Design 115\u003c\/p\u003e \u003cp\u003e9.2.1 Randomization 115\u003c\/p\u003e \u003cp\u003e9.2.2 Design-Based Estimation 118\u003c\/p\u003e \u003cp\u003e9.3 Application to Compositional Data 122\u003c\/p\u003e \u003cp\u003e9.3.1 Weighted Arithmetic and Geometric Means 123\u003c\/p\u003e \u003cp\u003e9.3.2 Closed Arithmetic Mean of Amounts 123\u003c\/p\u003e \u003cp\u003e9.3.3 Centred Log-Ratio of the Geometric Mean Composition 124\u003c\/p\u003e \u003cp\u003e9.3.4 Closed Geometric Mean Composition 124\u003c\/p\u003e \u003cp\u003e9.3.5 Example: Swiss Earnings Structure Survey (SESS) 125\u003c\/p\u003e \u003cp\u003e9.4 Discussion 126\u003c\/p\u003e \u003cp\u003eReferences 126\u003c\/p\u003e \u003cp\u003e10 Notes on the Scaled Dirichlet Distribution 128\u003cbr\u003e \u003ci\u003eGianna Serafina Monti, Glòria Mateu-Figueras and Vera Pawlowsky-Glahn\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 128\u003c\/p\u003e \u003cp\u003e10.2 Genesis of the Scaled Dirichlet Distribution 129\u003c\/p\u003e \u003cp\u003e10.3 Properties of the Scaled Dirichlet Distribution 131\u003c\/p\u003e \u003cp\u003e10.3.1 Graphical Comparison 131\u003c\/p\u003e \u003cp\u003e10.3.2 Membership in the Exponential Family 133\u003c\/p\u003e \u003cp\u003e10.3.3 Measures of Location and Variability 134\u003c\/p\u003e \u003cp\u003e10.4 Conclusions 136\u003c\/p\u003e \u003cp\u003eAcknowledgements 137\u003c\/p\u003e \u003cp\u003eReferences 137\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart III Theory – Algebra and Calculus\u003c\/b\u003e 139\u003c\/p\u003e \u003cp\u003e11 Elements of Simplicial Linear Algebra and Geometry 141\u003cbr\u003e \u003ci\u003eJuan José Egozcue, Carles Barceló-Vidal, Josep Antoni Martún-Fernández, Eusebi Jarauta-Bragulat, José Luis Dúaz-Barrero and Glòria Mateu-Figueras\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction 141\u003c\/p\u003e \u003cp\u003e11.2 Elements of Simplicial Geometry 142\u003c\/p\u003e \u003cp\u003e11.2.1 \u003ci\u003en\u003c\/i\u003e-Part Simplex 142\u003c\/p\u003e \u003cp\u003e11.2.2 Vector Space 143\u003c\/p\u003e \u003cp\u003e11.2.3 Centred Log-Ratio Representation 146\u003c\/p\u003e \u003cp\u003e11.2.4 Metrics 147\u003c\/p\u003e \u003cp\u003e11.2.5 Orthonormal Basis and Coordinates 149\u003c\/p\u003e \u003cp\u003e11.3 Linear Functions 151\u003c\/p\u003e \u003cp\u003e11.3.1 Linear Functions Defined on the Simplex 152\u003c\/p\u003e \u003cp\u003e11.3.2 Simplicial Linear Function Defined on a Real Space 153\u003c\/p\u003e \u003cp\u003e11.3.3 Simplicial Linear Function Defined on the Simplex 154\u003c\/p\u003e \u003cp\u003e11.4 Conclusions 156\u003c\/p\u003e \u003cp\u003eAcknowledgements 156\u003c\/p\u003e \u003cp\u003eReferences 156\u003c\/p\u003e \u003cp\u003e12 Calculus of Simplex-Valued Functions 158\u003cbr\u003e \u003ci\u003eJuan José Egozcue, Eusebi Jarauta-Bragulat and José Luis Díaz-Barrero\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e12.1 Introduction 158\u003c\/p\u003e \u003cp\u003e12.2 Limits, Continuity and Differentiability 161\u003c\/p\u003e \u003cp\u003e12.2.1 Limits and Continuity 161\u003c\/p\u003e \u003cp\u003e12.2.2 Differentiability 163\u003c\/p\u003e \u003cp\u003e12.2.3 Higher Order Derivatives 169\u003c\/p\u003e \u003cp\u003e12.3 Integration 171\u003c\/p\u003e \u003cp\u003e12.3.1 Antiderivatives. Indefinite Integral 171\u003c\/p\u003e \u003cp\u003e12.3.2 Integration of Continuous SV Functions 172\u003c\/p\u003e \u003cp\u003e12.4 Conclusions 174\u003c\/p\u003e \u003cp\u003eAcknowledgements 175\u003c\/p\u003e \u003cp\u003eReferences 175\u003c\/p\u003e \u003cp\u003e13 Compositional Differential Calculus on the Simplex 176\u003cbr\u003e \u003ci\u003eCarles Barceló-Vidal, Josep Antoni Martún-Fernández and Glòria Mateu-Figueras\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e13.1 Introduction 176\u003c\/p\u003e \u003cp\u003e13.2 Vector-Valued Functions on the Simplex 177\u003c\/p\u003e \u003cp\u003e13.2.1 Scale-Invariant Vector-Valued Functions on R\u003ci\u003en\u003c\/i\u003e + 177\u003c\/p\u003e \u003cp\u003e13.2.2 Vector-Valued Functions on \u003ci\u003eSn\u003c\/i\u003e 178\u003c\/p\u003e \u003cp\u003e13.3 \u003ci\u003eC\u003c\/i\u003e-Derivatives on the Simplex 178\u003c\/p\u003e \u003cp\u003e13.3.1 Derivative of a Scale-Invariant Vector-Valued Function on R\u003ci\u003en\u003c\/i\u003e + 178\u003c\/p\u003e \u003cp\u003e13.3.2 Directional \u003ci\u003eC\u003c\/i\u003e-Derivatives 180\u003c\/p\u003e \u003cp\u003e13.3.3 \u003ci\u003eC\u003c\/i\u003e-Derivative 182\u003c\/p\u003e \u003cp\u003e13.3.4 \u003ci\u003eC\u003c\/i\u003e-Gradient 184\u003c\/p\u003e \u003cp\u003e13.3.5 Critical Points of a \u003ci\u003eC\u003c\/i\u003e-Differentiable Real-Valued Function on \u003ci\u003eSn\u003c\/i\u003e 184\u003c\/p\u003e \u003cp\u003e13.4 Example: Experiments with Mixtures 185\u003c\/p\u003e \u003cp\u003e13.4.1 Polynomial of Degree One 185\u003c\/p\u003e \u003cp\u003e13.4.2 Polynomial of Degree Two 186\u003c\/p\u003e \u003cp\u003e13.4.3 Polynomial of Degree One in Logarithms 187\u003c\/p\u003e \u003cp\u003e13.4.4 A numerical Example 188\u003c\/p\u003e \u003cp\u003e13.5 Discussion 189\u003c\/p\u003e \u003cp\u003eAcknowledgements 190\u003c\/p\u003e \u003cp\u003eReferences 190\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart IV Applications\u003c\/b\u003e 191\u003c\/p\u003e \u003cp\u003e14 Proportions, Percentages, PPM: Do the Molecular Biosciences Treat Compositional Data Right? 193\u003cbr\u003e \u003ci\u003eDavid Lovell, Warren Müller, Jen Taylor, Alec Zwart and Chris Helliwell\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e14.1 Introduction 193\u003c\/p\u003e \u003cp\u003e14.2 The Omics Imp and Two Bioscience Experiment Paradigms 194\u003c\/p\u003e \u003cp\u003e14.3 The Impact of Compositional Constraints in the Omics 197\u003c\/p\u003e \u003cp\u003e14.3.1 Univariate Impact of Compositional Constraints 197\u003c\/p\u003e \u003cp\u003e14.3.2 Impact of Compositional Constraints on Multivariate\u003c\/p\u003e \u003cp\u003eDistance Metrics 199\u003c\/p\u003e \u003cp\u003e14.4 Impact of Compositional Constraints on Correlation and Covariance 201\u003c\/p\u003e \u003cp\u003e14.4.1 Compositional Constraints, Covariance, Correlation and Log-Transformed Data 202\u003c\/p\u003e \u003cp\u003e14.4.2 A Simulation Approach to Understanding the Impact of Closure 202\u003c\/p\u003e \u003cp\u003e14.5 Implications 204\u003c\/p\u003e \u003cp\u003e14.5.1 Gathering Information to Infer Absolute Abundance 204\u003c\/p\u003e \u003cp\u003e14.5.2 Analysing Compositional Omics Data Appropriately 205\u003c\/p\u003e \u003cp\u003eAcknowledgements 206\u003c\/p\u003e \u003cp\u003eReferences 206\u003c\/p\u003e \u003cp\u003e15 Hardy–Weinberg Equilibrium: A Nonparametric Compositional Approach 208\u003cbr\u003e \u003ci\u003eJan Graffelman and Juan José Egozcue\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e15.1 Introduction 208\u003c\/p\u003e \u003cp\u003e15.2 Genetic Data Sets 209\u003c\/p\u003e \u003cp\u003e15.3 Classical Tests for HWE 210\u003c\/p\u003e \u003cp\u003e15.4 A Compositional Approach 210\u003c\/p\u003e \u003cp\u003e15.5 Example 214\u003c\/p\u003e \u003cp\u003e15.6 Conclusion and Discussion 215\u003c\/p\u003e \u003cp\u003eAcknowledgements 215\u003c\/p\u003e \u003cp\u003eReferences 215\u003c\/p\u003e \u003cp\u003e16 Compositional Analysis in Behavioural and Evolutionary Ecology 218\u003cbr\u003e \u003ci\u003eMichele Edoardo Raffaele Pierotti and Josep Antoni Martún-Fernández\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e16.1 Introduction 218\u003c\/p\u003e \u003cp\u003e16.2 CODA in Population Genetics 219\u003c\/p\u003e \u003cp\u003e16.3 CODA in Habitat Choice 222\u003c\/p\u003e \u003cp\u003e16.4 Multiple Choice and Individual Variation in Preferences 224\u003c\/p\u003e \u003cp\u003e16.5 Ecological Specialization 228\u003c\/p\u003e \u003cp\u003e16.6 Time Budgets: More on Specialization 229\u003c\/p\u003e \u003cp\u003e16.7 Conclusions 231\u003c\/p\u003e \u003cp\u003eAcknowledgements 231\u003c\/p\u003e \u003cp\u003eReferences 231\u003c\/p\u003e \u003cp\u003e17 Flying in Compositional Morphospaces: Evolution of Limb Proportions in Flying Vertebrates 235\u003cbr\u003e \u003ci\u003eLuis Azevedo Rodrigues, Josep Daunis-i-Estadella, Glòria Mateu-Figueras and Santiago Thi´o-Henestrosa\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e17.1 Introduction 235\u003c\/p\u003e \u003cp\u003e17.2 Flying Vertebrates – General Anatomical and Functional Characteristics 236\u003c\/p\u003e \u003cp\u003e17.3 Materials 236\u003c\/p\u003e \u003cp\u003e17.4 Methods 238\u003c\/p\u003e \u003cp\u003e17.5 Aitchison Distance Disparity Metrics 239\u003c\/p\u003e \u003cp\u003e17.5.1 Intragroup Aitchison Distance 239\u003c\/p\u003e \u003cp\u003e17.5.2 Intergroup Aitchison Distance 240\u003c\/p\u003e \u003cp\u003e17.6 Statistical Tests 243\u003c\/p\u003e \u003cp\u003e17.7 Biplots 244\u003c\/p\u003e \u003cp\u003e17.7.1 Chiroptera 244\u003c\/p\u003e \u003cp\u003e17.7.2 Pterosauria 245\u003c\/p\u003e \u003cp\u003e17.8 Balances 246\u003c\/p\u003e \u003cp\u003e17.9 Size Effect 249\u003c\/p\u003e \u003cp\u003e17.10 Final Remarks 249\u003c\/p\u003e \u003cp\u003e17.10.1 All Groups 250\u003c\/p\u003e \u003cp\u003e17.10.2 Aves 250\u003c\/p\u003e \u003cp\u003e17.10.3 Pterosauria 250\u003c\/p\u003e \u003cp\u003e17.10.4 Chiroptera 251\u003c\/p\u003e \u003cp\u003eAcknowledgements 252\u003c\/p\u003e \u003cp\u003eReferences 252\u003c\/p\u003e \u003cp\u003e18 Natural Laws Governing the Distribution of the Elements in Geochemistry: The Role of the Log-Ratio Approach 255\u003cbr\u003e \u003ci\u003eAntonella Buccianti\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e18.1 Introduction 255\u003c\/p\u003e \u003cp\u003e18.2 Geochemical Processes and Log-Ratio Approach 256\u003c\/p\u003e \u003cp\u003e18.3 Log-Ratio Approach and Water Chemistry 258\u003c\/p\u003e \u003cp\u003e18.4 Log-Ratio Approach and Volcanic Gas Chemistry 261\u003c\/p\u003e \u003cp\u003e18.5 Log-Ratio Approach and Subducting Sediment Composition 263\u003c\/p\u003e \u003cp\u003e18.6 Conclusions 265\u003c\/p\u003e \u003cp\u003eAcknowledgements 265\u003c\/p\u003e \u003cp\u003eReferences 265\u003c\/p\u003e \u003cp\u003e19 Compositional Data Analysis in Planetology: The Surfaces of Mars and Mercury 267\u003cbr\u003e \u003ci\u003eHelmut Lammer, Peter Wurz, Josep Antoni Martún-Fernández and Herbert Iwo Maria Lichtenegger\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e19.1 Introduction 267\u003c\/p\u003e \u003cp\u003e19.1.1 Mars 267\u003c\/p\u003e \u003cp\u003e19.1.2 Mercury 269\u003c\/p\u003e \u003cp\u003e19.1.3 Analysis of Surface Composition 270\u003c\/p\u003e \u003cp\u003e19.2 Compositional Analysis of Mars’ Surface 270\u003c\/p\u003e \u003cp\u003e19.3 Compositional Analysis of Mercury’s Surface 274\u003c\/p\u003e \u003cp\u003e19.4 Conclusion 278\u003c\/p\u003e \u003cp\u003eAcknowledgement 278\u003c\/p\u003e \u003cp\u003eReferences 278\u003c\/p\u003e \u003cp\u003e20 Spectral Analysis of Compositional Data in Cyclostratigraphy 282\u003cbr\u003e \u003ci\u003eEulogio Pardo-Igúzquiza and Javier Heredia\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e20.1 Introduction 282\u003c\/p\u003e \u003cp\u003e20.2 The Method 283\u003c\/p\u003e \u003cp\u003e20.3 Case Study 285\u003c\/p\u003e \u003cp\u003e20.4 Discussion 287\u003c\/p\u003e \u003cp\u003e20.5 Conclusions 288\u003c\/p\u003e \u003cp\u003eAcknowledgement 288\u003c\/p\u003e \u003cp\u003eReferences 288\u003c\/p\u003e \u003cp\u003e21 Multivariate Geochemical Data Analysis in Physical Geography 290\u003cbr\u003e \u003ci\u003eJennifer McKinley and Christopher David Lloyd\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e21.1 Introduction 290\u003c\/p\u003e \u003cp\u003e21.2 Context 291\u003c\/p\u003e \u003cp\u003e21.3 Data 293\u003c\/p\u003e \u003cp\u003e21.4 Analysis 295\u003c\/p\u003e \u003cp\u003e21.5 Discussion 299\u003c\/p\u003e \u003cp\u003e21.6 Conclusion 300\u003c\/p\u003e \u003cp\u003eAcknowledgement 300\u003c\/p\u003e \u003cp\u003eReferences 300\u003c\/p\u003e \u003cp\u003e22 Combining Isotopic and Compositional Data: A Discrimination of Regions Prone to Nitrate Pollution 302\u003cbr\u003e \u003ci\u003eRoger Puig, Raimon Tolosana-Delgado, Neus Otero and Albert Folch\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e22.1 Introduction 302\u003c\/p\u003e \u003cp\u003e22.2 Study Area 303\u003c\/p\u003e \u003cp\u003e22.2.1 Maresme 304\u003c\/p\u003e \u003cp\u003e22.2.2 Osona 305\u003c\/p\u003e \u003cp\u003e22.2.3 Lluc¸an`es 305\u003c\/p\u003e \u003cp\u003e22.2.4 Empord`a 306\u003c\/p\u003e \u003cp\u003e22.2.5 Selva 306\u003c\/p\u003e \u003cp\u003e22.3 Analytical Methods 306\u003c\/p\u003e \u003cp\u003e22.4 Statistical Treatment 307\u003c\/p\u003e \u003cp\u003e22.4.1 Data Scaling 307\u003c\/p\u003e \u003cp\u003e22.4.2 Linear Discriminant Analysis 309\u003c\/p\u003e \u003cp\u003e22.4.3 Discriminant Biplots 310\u003c\/p\u003e \u003cp\u003e22.5 Results and Discussion 311\u003c\/p\u003e \u003cp\u003e22.6 Conclusions 314\u003c\/p\u003e \u003cp\u003eAcknowledgements 315\u003c\/p\u003e \u003cp\u003eReferences 315\u003c\/p\u003e \u003cp\u003e23 Applications in Economics 318\u003cbr\u003e \u003ci\u003eTim Fry\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e23.1 Introduction 318\u003c\/p\u003e \u003cp\u003e23.2 Consumer Demand Systems 319\u003c\/p\u003e \u003cp\u003e23.3 Miscellaneous Applications 322\u003c\/p\u003e \u003cp\u003e23.4 Compositional Time Series 323\u003c\/p\u003e \u003cp\u003e23.5 New Directions 323\u003c\/p\u003e \u003cp\u003e23.6 Conclusion 325\u003c\/p\u003e \u003cp\u003eReferences 325\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart V Software\u003c\/b\u003e 327\u003c\/p\u003e \u003cp\u003e24 Exploratory Analysis Using CoDaPack 3D 329\u003cbr\u003e \u003ci\u003eSantiago Thió-Henestrosa and Josep Daunis-i-Estadella\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e24.1 CoDaPack 3D Description 329\u003c\/p\u003e \u003cp\u003e24.2 Data Set Description 331\u003c\/p\u003e \u003cp\u003e24.3 Exploratory Analysis 333\u003c\/p\u003e \u003cp\u003e24.3.1 Numerical Analysis 333\u003c\/p\u003e \u003cp\u003e24.3.2 Biplot 334\u003c\/p\u003e \u003cp\u003e24.3.3 The Ternary Diagram 335\u003c\/p\u003e \u003cp\u003e24.3.4 Principal Component Analysis 336\u003c\/p\u003e \u003cp\u003e24.3.5 Balance-Dendrogram 336\u003c\/p\u003e \u003cp\u003e24.3.6 By Groups Description 338\u003c\/p\u003e \u003cp\u003e24.4 Summary and Conclusions 339\u003c\/p\u003e \u003cp\u003eAcknowledgements 340\u003c\/p\u003e \u003cp\u003eReferences 340\u003c\/p\u003e \u003cp\u003e25 robCompositions: An R-package for Robust Statistical Analysis of Compositional Data 341\u003cbr\u003e \u003ci\u003eMatthias Templ, Karel Hron and Peter Filzmoser\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e25.1 General Information on the R-package robCompositions 341\u003c\/p\u003e \u003cp\u003e25.1.1 Data Sets Included in the Package 342\u003c\/p\u003e \u003cp\u003e25.1.2 Design Principles 343\u003c\/p\u003e \u003cp\u003e25.2 Expressing Compositional Data in Coordinates 343\u003c\/p\u003e \u003cp\u003e25.3 Multivariate Statistical Methods for Compositional Data Containing Outliers 345\u003c\/p\u003e \u003cp\u003e25.3.1 Multivariate Outlier Detection 345\u003c\/p\u003e \u003cp\u003e25.3.2 Principal Component Analysis and the Robust Compositional Biplot 347\u003c\/p\u003e \u003cp\u003e25.3.3 Discriminant Analysis 350\u003c\/p\u003e \u003cp\u003e25.4 Robust Imputation of Missing Values 351\u003c\/p\u003e \u003cp\u003e25.5 Summary 354\u003c\/p\u003e \u003cp\u003eReferences 354\u003c\/p\u003e \u003cp\u003e26 Linear Models with Compositions in R 356\u003cbr\u003e \u003ci\u003eRaimon Tolosana-Delgado and Karl Gerald van den Boogaart\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e26.1 Introduction 356\u003c\/p\u003e \u003cp\u003e26.2 The Illustration Data Set 357\u003c\/p\u003e \u003cp\u003e26.2.1 The Data 357\u003c\/p\u003e \u003cp\u003e26.2.2 Descriptive Analysis of Compositional Characteristics 358\u003c\/p\u003e \u003cp\u003e26.3 Explanatory Binary Variable 360\u003c\/p\u003e \u003cp\u003e26.4 Explanatory Categorical Variable 363\u003c\/p\u003e \u003cp\u003e26.5 Explanatory Continuous Variable 365\u003c\/p\u003e \u003cp\u003e26.6 Explanatory Composition 367\u003c\/p\u003e \u003cp\u003e26.7 Conclusions 370\u003c\/p\u003e \u003cp\u003eAcknowledgement 371\u003c\/p\u003e \u003cp\u003eReferences 371\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIndex 373\u003c\/b\u003e\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402415841623,"sku":"9780470711354","price":75.56,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780470711354.jpg?v=1730480332","url":"https:\/\/bookcurl.com\/products\/compositional-data-analysis-9780470711354","provider":"Book Curl","version":"1.0","type":"link"}